Question

Two corners of a triangle have angles of `(7 pi )/ 12` and `pi / 8`. If one side of the triangle has a length of `6`, what is the longest possible perimeter of the triangle?

Answer 1

Perimeter # = a + b + c = 6 + 15.1445 + 12.4388 = 33.5833

Explanation:

Three angles are `(7pi)/12, pi/8, (7pi)/24`

To get the longest perimeter, side with length 6 should correspond to least angle of the triangle `(pi/8)`

`6/sin (pi/8) = b / sin ((7pi)/12) = c / sin ((7pi)/ 24)`

`b = (6*sin ((7pi)/12))/sin (pi/8) = 15.1445`

`c =( 6 * sin ((7pi)/24))/sin (pi/8) = 12.4388`

Perimeter # = a + b + c = 6 + 15.1445 + 12.4388 =33.5833